As the DSCF no longer exists, the Department of Health asked NICE to run a consultation on sex and relationships education. It's pretty much a re-run of the earlier consultation. I wrote this for work.
There is a lot more to say on the subject of PSHE and Dr Petra Boynton has covered all the main issues in her blog.
Friday, 30 July 2010
Sunday, 25 July 2010
Female Genital Mutilation in Britain
Female Genital Mutilation (FGM) is sometimes referred to as female circumcision although it is far more severe than the male version and should always be referred to as what it is - mutilation.
FGM has no health benefits. It involves removing and damaging healthy and normal female genital tissue, and interferes with the natural functions of girls' and women's bodies. It's done to ensure that the girls' future husbands can guarantee their bride is a virgin and to ensure fidelity. The causes are a complex mix of religious, social and cultural factors. Girls who are not cut can face being outcast from their societies and unable to find a husband. In essence, it is a way of controlling women's bodies and sexuality. It's said to reduce their libido, to be a sign of femininity and that women who are unmutilated are 'unclean' amongst other lies.
According to Forward UK, an anti-FGM charity, it's estimated that approximately 100-140 million African women have undergone FGM worldwide and each year, a further 3 million girls are estimated to be at risk in Africa alone. FGM also happens in the Middle East and Asian countries, and increasingly in Europe, Australia, New Zealand, the USA and Canada. Forward estimates that as many as 6,500 girls in the UK are at risk of FGM every year. The summer holidays are when many mutilations happen as they give the victims time to recover before going back to school in the autumn.
There are four types identified by the World Health Organisation, ranging from partial to total removal of the external female genitalia.
1. Clitoridectomy: partial or total removal of the clitoris and, in very rare cases, only the prepuce (the fold of skin surrounding the clitoris).
2. Excision: partial or total removal of the clitoris and the labia minora, with or without excision of the labia majora.
3. Infibulation: narrowing of the vaginal opening through the creation of a covering seal. The seal is formed by cutting and repositioning the inner, or outer, labia, with or without removal of the clitoris.
4. Other: all other harmful procedures to the female genitalia for non-medical purposes, e.g. pricking, piercing, incising, scraping and cauterizing the genital area.
However, an article in the BMJ questions the usefulness of these classifications, saying that 'The WHO classification fails to relate the defined forms to the severity of the operation'. For example: 'WHO classifies all forms that involve suturing as type III, regardless of whether the labia minora or majora have been cut. Therefore classification as type III does not indicate the extent of the mutilation that has been done. This is important, especially in investigations of FGM and complications'. Another problem is that 'Almost all studies about the prevalence and trends of ... (FGM) have been based on women self reporting their form of FGM. How this reported form corresponds to reality is unknown'. It concludes that 'The WHO should revise its classifications to relate the different forms more to the anatomical extent of the operation.' Far more research needs to be done to get useful statistics and to get rid of the ignorance, secrecy and silence around this subject.
FGM is traditionally done by an older woman with no medical training. Anaesthetics and antiseptic treatment are not generally used and cutting is usually done with basic tools like knives, scissors, scalpels, pieces of glass and razor blades. Often iodine or a mixture of herbs are placed on the wound to tighten the vagina and stop the bleeding. There have been cases of UK doctors willing to carry out the procedure. When caught, they have been struck off.
The most common age is between four and ten, although it appears to be falling. Some of the girls are taken abroad, some are mutilated in the UK. In some cases, there are 'cutting parties' with groups of girls mutilated together to save money.
Immediate risks are death from blood loss and infection, urinary and menstrual problems. Longer-term effects include extensive damage of the external reproductive system, uterus, vaginal and pelvic infections, cysts and neuromas, increased risk of Vesico Vaginal Fistula, complications in pregnancy and child birth, psychological damage, sexual dysfunction, difficulties in menstruation. Period blood can build up and clot, leading to serious, life-threatening infection. There are currently 16 clinics in the UK to deal with the damage.
None of the major world religions demands mutilation. Some religious leaders condemn it while others either turn a blind eye or endorse it. FGM is not limited to Muslims as it is practised in Christian communities too. It is thought to pre-date both religions and to have started in Egypt; type 3 mutilation (according to WHO classification) is also known as pharaonic circumcision. There is nothing in the Koran requiring FGM but there are hadeeths about it. For example: 'Circumcision is a commendable act for men (Sunnah) and is an honorable thing for women (Makromah)' and 'Prophet Muhammad is reported to have passed by a woman performing circumcision on a young girl. He instructed the woman by saying: "Cut off only the foreskin (outer fold of skin over the clitoris; the prepuce) but do not cut off deeply (i.e. the clitoris itself), for this is brighter for the face (of the girl) and more favorable with the husband'. While many Islamic scholars and leaders question these hadeeths, for anyone who wants an excuse, they can provide it.
The UK Prohibition of Female Circumcision Act 1985 makes it an offence to carry out FGM or to aid, abet or procure the service of another person. The Female Genital Mutilation Act 2003, makes it against the law for FGM to be performed anywhere in the world on UK permanent residents of any age and carries a maximum sentence of 14 years imprisonment. To date, no prosecutions have been made.
The UN Convention on the Rights of the Child (1989) requires 'all states to take all appropriate measures with a view to abolishing traditional practices prejudicial to the health of children' and Article 2 of the UN Declaration on the Elimination of Violence Against Women states that 'all violence against women shall be understood to include FGM and other traditional practices harmful to women'.
The UK police have set up Project Azure to combat the crime but have so far taken a soft approach. In 2007, the Met offered a £20,000 reward for information leading to arrest, with no success. Part of the problem is lack of research and the reliance on anecdotal evidence or statistics from doctors treating the after-effects because of the secrecy surrounding the procedure and successive governments' timidity in taking on 'cultural' issues. There have been debates about whether attempts to end the practice are Western cultural imperialism imposing its values on other cultures and whether cultural relativity means that the West has no right to comment on or condemn other people's traditions. Although there needs to be sensitivity in dealing with the subject, especially to avoid stigmatizing the women, this should not be an excuse for doing nothing. This is not some quaint 'ethnic' tradition, it's a non-consensual human rights violation
The West has its own history of fear and loathing of female genitals and sexuality. Freud stated in Sexuality and the Psychology of Love that the 'elimination of clitoral sexuality is a necessary precondition for the development of femininity', for example. In some extreme cases, clitorectomy was practised to prevent women masturbating or as a cure for hysteria and lesbianism.
More recently, women who have been made to feel there is something 'wrong' with their genitals are offered cosmetic surgery, to 'correct' large or assymetrical labia for example. According to one website, 'Many women dislike the large protuberant appearance of their labia. This may cause severe embarrassment with a sexual partner. Surgical labial reduction can greatly improve the aesthetic appearance of the abnormally enlarged labis.' One UK site says that 'It's not unusual for a woman to feel dissatisfied with her labia'.
Surgery is touted because it is a woman's 'right' to have beautiful genitalia - but also her duty if she wants to avoid shame and embarrassment. Although this in no way compares with the forced mutilation of girls and young women, it is an indicator that no society is immune from the pressure on women to conform to artificial norms of what are acceptable genitalia, creating yet another dissatisfaction with their bodies.
FGM has no health benefits. It involves removing and damaging healthy and normal female genital tissue, and interferes with the natural functions of girls' and women's bodies. It's done to ensure that the girls' future husbands can guarantee their bride is a virgin and to ensure fidelity. The causes are a complex mix of religious, social and cultural factors. Girls who are not cut can face being outcast from their societies and unable to find a husband. In essence, it is a way of controlling women's bodies and sexuality. It's said to reduce their libido, to be a sign of femininity and that women who are unmutilated are 'unclean' amongst other lies.
According to Forward UK, an anti-FGM charity, it's estimated that approximately 100-140 million African women have undergone FGM worldwide and each year, a further 3 million girls are estimated to be at risk in Africa alone. FGM also happens in the Middle East and Asian countries, and increasingly in Europe, Australia, New Zealand, the USA and Canada. Forward estimates that as many as 6,500 girls in the UK are at risk of FGM every year. The summer holidays are when many mutilations happen as they give the victims time to recover before going back to school in the autumn.
There are four types identified by the World Health Organisation, ranging from partial to total removal of the external female genitalia.
1. Clitoridectomy: partial or total removal of the clitoris and, in very rare cases, only the prepuce (the fold of skin surrounding the clitoris).
2. Excision: partial or total removal of the clitoris and the labia minora, with or without excision of the labia majora.
3. Infibulation: narrowing of the vaginal opening through the creation of a covering seal. The seal is formed by cutting and repositioning the inner, or outer, labia, with or without removal of the clitoris.
4. Other: all other harmful procedures to the female genitalia for non-medical purposes, e.g. pricking, piercing, incising, scraping and cauterizing the genital area.
However, an article in the BMJ questions the usefulness of these classifications, saying that 'The WHO classification fails to relate the defined forms to the severity of the operation'. For example: 'WHO classifies all forms that involve suturing as type III, regardless of whether the labia minora or majora have been cut. Therefore classification as type III does not indicate the extent of the mutilation that has been done. This is important, especially in investigations of FGM and complications'. Another problem is that 'Almost all studies about the prevalence and trends of ... (FGM) have been based on women self reporting their form of FGM. How this reported form corresponds to reality is unknown'. It concludes that 'The WHO should revise its classifications to relate the different forms more to the anatomical extent of the operation.' Far more research needs to be done to get useful statistics and to get rid of the ignorance, secrecy and silence around this subject.
FGM is traditionally done by an older woman with no medical training. Anaesthetics and antiseptic treatment are not generally used and cutting is usually done with basic tools like knives, scissors, scalpels, pieces of glass and razor blades. Often iodine or a mixture of herbs are placed on the wound to tighten the vagina and stop the bleeding. There have been cases of UK doctors willing to carry out the procedure. When caught, they have been struck off.
The most common age is between four and ten, although it appears to be falling. Some of the girls are taken abroad, some are mutilated in the UK. In some cases, there are 'cutting parties' with groups of girls mutilated together to save money.
Immediate risks are death from blood loss and infection, urinary and menstrual problems. Longer-term effects include extensive damage of the external reproductive system, uterus, vaginal and pelvic infections, cysts and neuromas, increased risk of Vesico Vaginal Fistula, complications in pregnancy and child birth, psychological damage, sexual dysfunction, difficulties in menstruation. Period blood can build up and clot, leading to serious, life-threatening infection. There are currently 16 clinics in the UK to deal with the damage.
None of the major world religions demands mutilation. Some religious leaders condemn it while others either turn a blind eye or endorse it. FGM is not limited to Muslims as it is practised in Christian communities too. It is thought to pre-date both religions and to have started in Egypt; type 3 mutilation (according to WHO classification) is also known as pharaonic circumcision. There is nothing in the Koran requiring FGM but there are hadeeths about it. For example: 'Circumcision is a commendable act for men (Sunnah) and is an honorable thing for women (Makromah)' and 'Prophet Muhammad is reported to have passed by a woman performing circumcision on a young girl. He instructed the woman by saying: "Cut off only the foreskin (outer fold of skin over the clitoris; the prepuce) but do not cut off deeply (i.e. the clitoris itself), for this is brighter for the face (of the girl) and more favorable with the husband'. While many Islamic scholars and leaders question these hadeeths, for anyone who wants an excuse, they can provide it.
The UK Prohibition of Female Circumcision Act 1985 makes it an offence to carry out FGM or to aid, abet or procure the service of another person. The Female Genital Mutilation Act 2003, makes it against the law for FGM to be performed anywhere in the world on UK permanent residents of any age and carries a maximum sentence of 14 years imprisonment. To date, no prosecutions have been made.
The UN Convention on the Rights of the Child (1989) requires 'all states to take all appropriate measures with a view to abolishing traditional practices prejudicial to the health of children' and Article 2 of the UN Declaration on the Elimination of Violence Against Women states that 'all violence against women shall be understood to include FGM and other traditional practices harmful to women'.
The UK police have set up Project Azure to combat the crime but have so far taken a soft approach. In 2007, the Met offered a £20,000 reward for information leading to arrest, with no success. Part of the problem is lack of research and the reliance on anecdotal evidence or statistics from doctors treating the after-effects because of the secrecy surrounding the procedure and successive governments' timidity in taking on 'cultural' issues. There have been debates about whether attempts to end the practice are Western cultural imperialism imposing its values on other cultures and whether cultural relativity means that the West has no right to comment on or condemn other people's traditions. Although there needs to be sensitivity in dealing with the subject, especially to avoid stigmatizing the women, this should not be an excuse for doing nothing. This is not some quaint 'ethnic' tradition, it's a non-consensual human rights violation
The West has its own history of fear and loathing of female genitals and sexuality. Freud stated in Sexuality and the Psychology of Love that the 'elimination of clitoral sexuality is a necessary precondition for the development of femininity', for example. In some extreme cases, clitorectomy was practised to prevent women masturbating or as a cure for hysteria and lesbianism.
More recently, women who have been made to feel there is something 'wrong' with their genitals are offered cosmetic surgery, to 'correct' large or assymetrical labia for example. According to one website, 'Many women dislike the large protuberant appearance of their labia. This may cause severe embarrassment with a sexual partner. Surgical labial reduction can greatly improve the aesthetic appearance of the abnormally enlarged labis.' One UK site says that 'It's not unusual for a woman to feel dissatisfied with her labia'.
Surgery is touted because it is a woman's 'right' to have beautiful genitalia - but also her duty if she wants to avoid shame and embarrassment. Although this in no way compares with the forced mutilation of girls and young women, it is an indicator that no society is immune from the pressure on women to conform to artificial norms of what are acceptable genitalia, creating yet another dissatisfaction with their bodies.
Saturday, 24 July 2010
Noah's Ark Zoo wins an award
Noah's Ark Zoo in Wraxall, North Somerset has won a Learning Outside the Classroom Quality badge for its schools programme.
This is surprising for two reasons.
Firstly, an investigation by the Captive Animals Protection Society (CAPS) and the BBC Programme Inside Out found that the zoo was breeding tigers for a controversial circus owner and that staff were under strict orders not to tell anyone.
One of the tigers died 10 days after giving birth to four cubs, one of which also died. The zoo claimed that she died from Feline Infectious Peritonitis but there was no proper post-mortem. The tiger's head, paws and skin were cut off and the body was buried in breach of animal disposal legislation.
A woman working undercover for CAPS found the head in a freezer. According to CAPS, the zoo's education officer, also a qualified vet, admitted to her that the burial was illegal, that she turned a blind eye and that no proper examination was done, even to check if the tiger had died of something infectious. The education officer told the undercover worker that the tiger's owner (the circus) wanted the head and paws.
As a result of the CAPS investigation, the zoo lost its membership of the trade body BIAZA - the British and Irish Association of Zoos and Aquariums. Nevertheless, North Somerset Council has recently approved plans for an elephant house.
Secondly, it's a creationist zoo. The website says:
'Undoubtedly, Darwin helped science to see that nature is continually changing, but along with this great progress there began a subsequent movement to remove any notion of God from our understanding of life. This is unjustified and we look to put the case for the Creator across to those who wish to investigate'
and
'Is it right for Darwin's evolutionary theory to be portrayed as "fact" in today's scientific media and the idea of God generally abandoned?'
and
'Important scientific theories have been proposed and much research done on the subject, but these, while widely accepted, have serious problems with them. After looking at the current explanations for origins and evolution; it is our view that the evidence available points to widespread evolution after an initial Creation by God'.
And much more.
According to the LOTC website, the award is judged on 'six high level generic quality indicators'. They are:
1. The provider has a process in place to assist users to plan the learning experience effectively;
2. The provider provides accurate information about its offer;
3. The provider provides activities or experiences which meet learner needs;
4. The provider reviews the experience and acts upon feedback;
5. The provider meets the needs of users; and
6. The provider has safety management processes in place to manage risk effectively.
As long as your learner needs don't include animal welfare, science or the meaning of the words 'fact', 'evidence' and 'theory', then you're fine. Are teachers keen for pupils to learn that God made everything or do they ignore that part as long as the kiddies can look at the nice animals?
The Bristol Animal Rights Collective has a petition against the zoo and holds regular protests outside. There's a big demo on August 30th.
Incidentally, according to Genesis 7:2-3, the animals didn't all go in two by two. The clean went in seven by seven and the unclean two by two. The seventh of each clean species was sacrificed once they reached dry land (v20). Which must have taken quite a long time.
UPDATE 18 August 2010
My comments to a Welsh newspaper on the zoo.
Thursday, 15 July 2010
Vatican Causes Cancer?
The Vatican has been accused of giving children cancer. Highly amusing as it is to think of a radioactive Pope spreading Vaticancer, he's too busy with all the child abuse cover-ups and conning the UK taxpayer into spending up to £100 million on his visit to waste energy emitting Papal Death Rays. He is getting on a bit, after all.
Professor Andrea Micheli has written a 300 page report focussing on 19 deaths from leukemia or lymphoma between 1980 and 2003 in the Cesano area north of Rome. Vatican Radio has 60 masts nearby in Santa Maria di Galeria. Micheli's investigation was ordered by a Roman court five years ago after concerns were raised about an increased incidence of cancer in the area. It's not clear exactly who was concerned.
He claims that children under 14 living within a 7.5km radius of the masts have a raised cancer risk. As a result of his research, six Vatican Radio officials are under investigation for manslaughter.
The charges mean that this is not just yet another lame conspiracy theorist attempt to link masts or electromagnetic waves and cancer or the usual Daily Mail cancer scare.
Quackwatch has very thoroughly shown why there is no conclusive link.
Moreover, the Italian Navy also operates masts in the area but Micheli insists that it's the Vatican masts that are to blame. Perhaps there is some added toxic ingredient being emitted because of what they are broadcasting. As Quackwatch says:'what they emit is not understood by the public. Nor can they be felt, tasted, seen or touched. This makes them mysterious, easily portrayable as threatening'. Temptation to draw a parallel with certain aspects of religion will be resisted.
There are other problems with Micheli's findings. Firstly, the research was submitted to a court, not for peer review. The contents were leaked.
A research paper that is available without leakage in the American Journal of Epidemiology called Adult and Childhood Leukemia near a high-powered radio station in Rome, Italy finds that rates were higher than expected but that 'The study has limitations because of the small number of cases and the lack of exposure data.' It adds that 'no causal implication can be drawn'.
And the Lancet finds that: 'In the European population, about 1% of all malignant neoplasms arise in patients younger than 20 years. This low frequency represents a major difficulty for studies of putative risk factors'.
An article in The Hematology Journal called Expected number of childhood cancers in Italy from 2001 to 2015 states: 'The total number of children with incident cancer in Italy has never been specifically estimated. Specialized population-based Childhood Cancer Registries have only been operating in Piedmont (CCRP) and in the Marche region, while general population cancer registries cover about 20% of the Italian population'.
This means that there is insufficient data to tell if cancer rates have gone up above the expected rate compared with other mast-free parts of Italy. It's hard to gauge what's higher than expected when there is no accurate definition of 'expected'.
Leukemia and lymphoma are the commonest childhood cancers. Italy has nearly the highest rate of them in the whole world.
In Europe, the overall incidence increased by 1% a year from 1970-99 in children and by 1.5% in adolescents. The average incidence in Europe is 140 per million for children up to 14. That's 1.4 children per ten thousand. According to the American Journal of Epidemiology research, nearly 50,000 people live in a 10km area around the station.
[edited 22/3/11: In the Perugia region, about 150km north of Rome, for example, around 1.3 children in ten thousand get leukemia or lymphoma every year.
Nineteen children got leukemia or lymphoma in a twenty three year period in the Cesano area. In the Perugia region in the same period, you would expect just under 30 children to get them.]
While the data from these various sources are not directly comparable, it looks very much like nineteen deaths is not a suspicious figure.
This is probably the one and only time I will ever defend the Vatican.
Professor Andrea Micheli has written a 300 page report focussing on 19 deaths from leukemia or lymphoma between 1980 and 2003 in the Cesano area north of Rome. Vatican Radio has 60 masts nearby in Santa Maria di Galeria. Micheli's investigation was ordered by a Roman court five years ago after concerns were raised about an increased incidence of cancer in the area. It's not clear exactly who was concerned.
He claims that children under 14 living within a 7.5km radius of the masts have a raised cancer risk. As a result of his research, six Vatican Radio officials are under investigation for manslaughter.
The charges mean that this is not just yet another lame conspiracy theorist attempt to link masts or electromagnetic waves and cancer or the usual Daily Mail cancer scare.
Quackwatch has very thoroughly shown why there is no conclusive link.
Moreover, the Italian Navy also operates masts in the area but Micheli insists that it's the Vatican masts that are to blame. Perhaps there is some added toxic ingredient being emitted because of what they are broadcasting. As Quackwatch says:'what they emit is not understood by the public. Nor can they be felt, tasted, seen or touched. This makes them mysterious, easily portrayable as threatening'. Temptation to draw a parallel with certain aspects of religion will be resisted.
There are other problems with Micheli's findings. Firstly, the research was submitted to a court, not for peer review. The contents were leaked.
A research paper that is available without leakage in the American Journal of Epidemiology called Adult and Childhood Leukemia near a high-powered radio station in Rome, Italy finds that rates were higher than expected but that 'The study has limitations because of the small number of cases and the lack of exposure data.' It adds that 'no causal implication can be drawn'.
And the Lancet finds that: 'In the European population, about 1% of all malignant neoplasms arise in patients younger than 20 years. This low frequency represents a major difficulty for studies of putative risk factors'.
An article in The Hematology Journal called Expected number of childhood cancers in Italy from 2001 to 2015 states: 'The total number of children with incident cancer in Italy has never been specifically estimated. Specialized population-based Childhood Cancer Registries have only been operating in Piedmont (CCRP) and in the Marche region, while general population cancer registries cover about 20% of the Italian population'.
This means that there is insufficient data to tell if cancer rates have gone up above the expected rate compared with other mast-free parts of Italy. It's hard to gauge what's higher than expected when there is no accurate definition of 'expected'.
Leukemia and lymphoma are the commonest childhood cancers. Italy has nearly the highest rate of them in the whole world.
In Europe, the overall incidence increased by 1% a year from 1970-99 in children and by 1.5% in adolescents. The average incidence in Europe is 140 per million for children up to 14. That's 1.4 children per ten thousand. According to the American Journal of Epidemiology research, nearly 50,000 people live in a 10km area around the station.
[edited 22/3/11: In the Perugia region, about 150km north of Rome, for example, around 1.3 children in ten thousand get leukemia or lymphoma every year.
Nineteen children got leukemia or lymphoma in a twenty three year period in the Cesano area. In the Perugia region in the same period, you would expect just under 30 children to get them.]
While the data from these various sources are not directly comparable, it looks very much like nineteen deaths is not a suspicious figure.
This is probably the one and only time I will ever defend the Vatican.
Thursday, 8 July 2010
Hyperbolic Crochet
In 1997 a mathematician at Cornell figured out how to make a model of hyperbolic space that her students could handle so they could understand the concept better. Dr Daina Taimina got the idea from William Thurston but his paper models were too fragile to be of practical use. Crochet to the rescue.
With hyperbolic space, as you move away from a point, the space around it expands exponentially. While all spheres have the same form, hyperbolic surfaces can differ substantially. This quality is characterized by the radius of the plane; the more crenellated the surface, the smaller its radius and the flatter the surface, the greater its radius. A regular Euclidean plane can be thought of as a hyperbolic plane of infinite radius.
To show you what this means in practice, here are my own attempts. This is what one looks like after just two rows of crochet:
And after four rows:
And six:
And eight (at which point, I ran out of yarn):
The width is 9cm and the edge measures over 2.5m. Dr Tamina's biggest one had a width of 4 inches, a perimeter length of 369 inches and weighed nearly a pound.
The photos are not great quality, but you get the idea. There are some better quality ones here. For mathematicians, an increase is made every Nth stitch so the number of stitches from one row to the next is in the constant ratio N to N+1. For crocheters, I used a 3.5mm needle, double acrylic yarn and started with a ring of 6 stitches then increased in every stitch, working in double (or, if you're American, single).
There are examples of hyperbolic geometry in nature, like lettuce, kelp, sea slugs, flatworms and nudibranches. Margaret and Christine Wertheim of the Institute for Figuring have made a crocheted coral reef with kelps, anemones, sea slugs and corals by using variations and permutations of the basic algorithm. Crocheters all over the world have contributed and there are now many sub-reefs, like the Bleached Reef:
After which, my own little sea creature looks a bit lonely:
It's really really easy to do. Who says maths can't be fun?
Next time, the science of kittens and pink things.
Thanks to my crochet guru for this one.
With hyperbolic space, as you move away from a point, the space around it expands exponentially. While all spheres have the same form, hyperbolic surfaces can differ substantially. This quality is characterized by the radius of the plane; the more crenellated the surface, the smaller its radius and the flatter the surface, the greater its radius. A regular Euclidean plane can be thought of as a hyperbolic plane of infinite radius.
To show you what this means in practice, here are my own attempts. This is what one looks like after just two rows of crochet:
And after four rows:
And six:
And eight (at which point, I ran out of yarn):
The width is 9cm and the edge measures over 2.5m. Dr Tamina's biggest one had a width of 4 inches, a perimeter length of 369 inches and weighed nearly a pound.
The photos are not great quality, but you get the idea. There are some better quality ones here. For mathematicians, an increase is made every Nth stitch so the number of stitches from one row to the next is in the constant ratio N to N+1. For crocheters, I used a 3.5mm needle, double acrylic yarn and started with a ring of 6 stitches then increased in every stitch, working in double (or, if you're American, single).
There are examples of hyperbolic geometry in nature, like lettuce, kelp, sea slugs, flatworms and nudibranches. Margaret and Christine Wertheim of the Institute for Figuring have made a crocheted coral reef with kelps, anemones, sea slugs and corals by using variations and permutations of the basic algorithm. Crocheters all over the world have contributed and there are now many sub-reefs, like the Bleached Reef:
After which, my own little sea creature looks a bit lonely:
It's really really easy to do. Who says maths can't be fun?
Next time, the science of kittens and pink things.
Thanks to my crochet guru for this one.
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